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@Jeff That's a very broad question, and I don't really know what you're after. Are you asking from a reader's perspective or from a writer's perspective? This sounds like you're asking how to be a good fiction writer, and that's a huge question.
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GillesMay 5 '11 at 20:42

Further to @Gilles's comment, if this is about writing, then it's off-topic. If it's not about writing, could you edit so that's more clear?
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Tony MeyerMay 5 '11 at 23:15

8 Answers
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Basically, anything that the reader considers implausible when he's already suspending disbelief, can spoil the illusion and break that suspension. The key issue to understand is that up to a certain point, your story is exposing the world of the story, and explaining what's allowed and what isn't. Anything you establish clearly, the reader will be willing to accept, and suspend disbelief over. Anything implausible that you don't explain, or suggest can be explained (perhaps later), is not "protected", and can prompt readers to feel that the story is nonsensical or contrived - not in the agreed-upon, "protected" premise, but in the reasonable flow of events and consequences from that premise.

What, precisely, seems implausible may be highly individual. Here are major issues in my experience.

Setting rules are inconsistent or unclear: An SF/F reader will generally be willing to accept bizarre and impossible world constructions, as long as they are internally consistent. But if your stardates don't match up with each other, or if something impossible turns out to be possible with no real justification, then the reader senses that your rules are arbitrary and that the author does not feel bound by his own rules. The same thing happens if he can't figure out what your rules are meant to be to begin with. It's like playing a game somebody invented where he gets to change the rules all the time, and then declare himself the winner if he's losing anyway.

Excessive and/or unacknowledged inconsistency with the real world: In the real world, time travel is almost certainly objectively impossible; that doesn't mean you can't write time travel stories. But if you do something that's impossible in the real world without explaining it, or making it clear that this is an interesting difference from real-life, and you-the-author are aware of this, then you come across as ignorant. The reader has difficulty trusting in your story. This could be scientific knowledge ("you couldn't really do that"), local knowledge ("that city doesn't really look like that"), social knowledge ("people don't _really act that way"), etc., etc.

Coincidence as a plot development: If anything immensely unlikely happens, it's best for it to happen at the beginning - as part of the premise. Using coincidence as a plot development can feel contrived - since it's not really a coincidence, but fiat on the author's side, the reader can sense that the author is deliberately manipulating the story in implausible, artificial directions, and he loses faith in the plot as being plausible, natural, and thus significant.

Unjustified references to real-world elements: In fantasy and science fiction, direct references to the real world can be very distracting. They have no more reason to dwell on, say, 21st century politics than we have to dwell on 13th century politics. It's unlikely that 2000 years from now, all spaceships will be named for current SF writers (and no future ones...). Even things that are similar can provoke this reaction - e.g. you don't want to name your fantasy princess "Diana" even if "Diana" is a perfectly fine name and it makes perfect sense for there to be a "Princess Diana" in your world. References to the real world, our world, throw the reader out of the story world.

Most of these issues can be solved by sufficient set-up - if you establish the unbelievable premise in a clear and plausible manner, it ceases to be unbelievable. But if you don't need something that's tough to justify, then avoiding it to begin with is often wise.

Seems to me that consistency is a big thing. Internal consistency and external consistency.

External consistency: on Numb3rs, they use real mathematical jargon assuming people will not understand it and will accept it at the Wikipedia level of understanding. But I actually do understand many of the techniques they talk about and they simply cannot be used in the manner they describe, crashing my belief to the ground.

Internal inconsistency: Bones, where they work in the present day with overall present-day technology, except for this holographic display that has elaborate animations programmed into it by an artist. Huh? If the show was full of futuristic technology in some secret government lab, or if it took place in the future, and if the artist were not the only non-geek on staff, it might be believable, but it stands out like a sore thumb.

Great examples. If you haven't watched it in a while, they really scaled back the use of that stupid holographic display on Bones after the first couple of seasons. I can't remember the last time they used it.
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Bill the LizardMay 5 '11 at 19:02

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Just wanted to tack on that 'external consistency', as explained above, is not limited to specialized knowledge; generally, people expect the fictitious world to behave like the real world except insofar as the rules are explicitly being broken. For example, Superman flying around and lifting massive weights doesn't break suspension of disbelief; Superman lifting an entire building by a corner without the building falling apart does break suspension of disbelief.
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AsmorMay 5 '11 at 19:53

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A more broad example of the 3D display is every cop show where they 'enhance' a 8x8 pixel image of a criminal into a ultra high resolution image (usually from a slightly different angle somehow).
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SamMay 5 '11 at 20:53

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@Wayne: I think it has a lot to do with "okay, that's not probable but I guess it's possible" instead of "no way in hell is that possible."
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Ralph GallagherMay 6 '11 at 1:53

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@Wayne, I just thought of one of the worst offenders. Product placement. Specifically, when the whole show stops, to talk about the product. "Oh, I'll just use the hands-free dialing feature on my new car." Bones does this, as well as many others, and it's much worse than the hologram thing. That doesn't bring the show to a crashing halt, like the advertising does.
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SamMay 10 '11 at 13:00

There are two failures of storytelling that can cause me to lose my suspension of disbelief:

Violating Established Rules

In Act I through the first half of Act II, the story should establish the rules by which this fantasy or scifi world operates. This is usually told from the perspective of the protagonist, who is thrown into this new reality along with the audience. A mentor character will often be introduced to teach the rules.

In the latter part of the story, no new rules should be introduced nor should the established rules be violated. The introduction of new rules at the last minute is an example of deus ex machina, which is not viewed as good storytelling. By establishing the rules early and sticking to them, it gives the audience a framework for what to expect for the rest of the story.

NOTE: You might be able to get away
with breaking/bending the rules if you
provide adequate foreshadowing that
the original rules might be false
and/or have loopholes.

Positive Example: The Matrix (part I)

Once Neo leaves the Matrix, Morpheus teaches him how the Matrix works. He then provides a bit of foreshadowing: most people can't break the rules, but Morpheus believes Neo can.

NOTE: These rules were broken in the
sequels without adequate explanation
of why. Totally ruined it for me.

Negative Example: Superman II

Lois learns that Clark Kent is Superman during the course of the movie. At the end, he kisses her and she completely forgets this one fact (and the events that occurred during the course of the movie, I suppose). Truly sloppy writing. The writers set up an extremely dramatic situation--the secret of Superman's identity is out. And instead of allowing this revelation to drive the story, they make it completely go away without any consequences to any of the characters involved.

It's just like a reset button on a video game: good for games, bad for storytelling.

Poorly Written Characters

I can suspend my disbelief to cover some crazy violations of physical reality as long as the characters are compelling. When the audience is caught up in the character's emotional journey, the details just aren't as important.

Positive Example: Spiderman II

In this movie, Peter Parker loses his superpowers in a way that is never fully explained within the context of the rules of the "Spiderman reality." It turns out that the disappearing powers are a physical manifestation of the character's internal struggle--and it works! We don't need to know more than what is given. If the writing and acting behind this character had not been as believable, this lack of explanation would have kicked me out of the experience.

Negative Example: Nearly every Michael Bay movie

Simplistic one-dimensional characters who are parodies of themselves. They make choices that are not believable within the context of human nature.

Specifically, the movie Armageddon. By the midpoint, I was noticing and getting highly annoyed by violations of physics. I had already been kicked far enough out of the story by that point to start nit-picking the details. I didn't care about the characters anymore.

Suspension of disbelief is a requirement of most fiction, and not just because of accepting the fantastic. It's because the story the author is telling is fictitious. It never happened, but as an author you're trying to create something real enough to fool the reader.

Therefore, if you want to break suspension of disbelief, introduce a plot hole.

Plot holes take on a number of forms, essentially because something integral to the story has not been explained adequately, or because there is an inconsistency.

Characters behaving in a way that is illogical or unlikely, events occurring that are near impossible, facts that are incorrect, logical inconsistencies and contradictions in the storyline, things happening for no reason - all of these result in plot holes, and will cause most readers to stop dead in their tracks.

To take an example you gave of "magic works", we suspend our disbelief because magic will have a set of rules attached that are outlined in the story. However, if the author breaks those rules without sufficient explanation, the book becomes kindling for the fireplace. And if it didn't have rules, we'd be less likely to accept it, because then anyone could do it, and anything would be possible since there are no limits.

Another example: a group of people are trapped in a warehouse with the doors bolted. There's a bomb. They spend their time trying to dismantle the bomb. It goes off, one person dies ... except we know that there's a giant window on one side of the wall, so why not smash it open, climb out, and escape to safety? (This actually happened in an episode of CSI, totally killed it for me).

Good fiction keeps suspension of disbelief because they are consistent, logical, explanatory, and follow the laws of the universe within which that story takes place.

The creation of the universe is where suspension of disbelief is allowed. Violating the rules/laws/physics of an already created world breaks the suspension of disbelief.

For example, most of what James Bond does in the movies is just not possible in real life. However, because it is a James Bond movie and the world created around the character allows for it, we are willing to suspend our disbelief. However, if THOSE rules are broken, say if James Bond suddenly flies without using a specialized gadget, then that breaks the spell.

Another way to look at it is, we accept that Luke can use the Force, but we will not accept that James Bond can use the Force, because it is a "real" thing in the Star Wars world, but it is not a "real" thing in the James Bond world.

Obvious plot holes - when I reach a point in the film or novel were the writer either failed to see the plot holes he was creating or worse hopes that the his audience has failed to see them that completely ruins my suspension of disbelief.

Weak or nonexistent characterizations - if I'm provided with no reason to be concerned about the characters in the film were a novel then at that point there is no reason for me to suspend my disbelief.

Too many continuity or grammatical errors - When a work of art poorly assembled and poorly edited, a completely distracts me from the story that it's telling.

Lack of research will often break the artificial realism. Sometimes it's hard to tell the difference between insufficient research and the author didn't care.

Case in point: The Crystal Singer by Anne MacAffrey. Central to the universe is the idea of a natural mineral on one planet that responds to "perfect pitch". Except "perfect pitch" is a furphy created by human history. Nature will create octaves, perfect fourths and fifths (and maybe a few more), but the western even tempered scale is entirely artificial. when I learnt about that, it quite broke my enjoyment of the novel.

For me, it boils down to: Are the sentences and paragraphs well structured and is there enough detail? Too many "He said" or "said so and so" and I have trouble staying in the realm of the story. R.A. Salvatore is definitely an author that keeps me in his stories with great sentence structure and a wealth of details.